Introduction to Calculus Course Syllabus

Overview: This course offers a rigorous yet accessible introduction to calculus, designed for students preparing for advanced studies in STEM fields. Over approximately 12-16 weeks of part-time study (8-10 hours per week), learners will build a strong foundation in differential and integral calculus, emphasizing both theoretical understanding and practical applications. The course balances core concepts with problem-solving techniques, preparing students for careers or further education in engineering, data science, physics, and economics.

Module 1: Functions and Limits

Estimated time: 15 hours

• Review of algebraic and transcendental functions
• Graphical and analytical understanding of limits
• Concept of continuity
• Intermediate Value Theorem

Module 2: Derivatives

Estimated time: 20 hours

• Derivative as instantaneous rate of change
• Differentiation rules: power, product, quotient
• Chain rule
• Tangent lines and velocity problems

Module 3: Applications of Derivatives

Estimated time: 20 hours

• Optimization problems
• Curve sketching: increasing/decreasing, concavity
• Related rates
• L'Hôpital's Rule

Module 4: Integration

Estimated time: 25 hours

• Riemann sums and definite integrals
• Antiderivatives and indefinite integrals
• Integration techniques
• Fundamental Theorem of Calculus

Module 5: Final Project

Estimated time: 10 hours

• Solve real-world optimization and rate problems using derivatives
• Apply integration to compute accumulated quantities
• Submit a comprehensive problem set demonstrating mastery of core concepts

Prerequisites

• Strong foundation in algebra
• Familiarity with pre-calculus functions
• Basic understanding of trigonometric and exponential functions

What You'll Be Able to Do After

• Compute and interpret derivatives of algebraic and transcendental functions
• Solve optimization and related rates problems
• Evaluate definite integrals and apply the Fundamental Theorem of Calculus
• Analyze functions using continuity, limits, and curve behavior
• Build a solid mathematical foundation for advanced STEM coursework